Some Results on the Cte Based Capital Allocation Rule
Insurance: Mathematics and Economics, Vol. 42, pp. 855-863, 2008
10 Pages Posted: 1 Jun 2006 Last revised: 14 Mar 2009
Date Written: January 27, 2006
Tasche (1999) introduces a capital allocation principle where the capital allocated to each risk unit can be expressed in terms of its contribution to the conditional tail expectation (CTE) of the aggregate risk.
Panjer (2002) derives a closed-form expression for this allocation rule in the multivariate normal case. Landsman & Valdez (2003) generalise Panjer's result to the class of multivariate elliptical distributions.
In this paper we provide an alternative and simpler proof for the CTE based allocation formula in the elliptical case. Furthermore, we derive accurate and easy computable closed-form approximations for this allocation formula for sums that involve normal and lognormal risks.
Keywords: Capital allocation, CTE, risk measure, coherent allocation, elliptical
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